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Problem 1 (50 pts) An infinitely long cylindrical container has a cross section area of radius R, and is placed horizontally with y gravity being in the -y direction, as shown in the figure

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Problem 1 (50 pts) An infinitely long cylindrical container has a cross section area of radius R, and is placed horizontally with y gravity being in the -y direction, as shown in the figure. The cylinder is 50% filled with water (the shaded part), with density p. The other 50% of the volume in the cylinder is filled R with air with constant pressure of p = Po. The length of the cylindrical container in the axial direction is W. X a) (10 pts) Starting from Newton's 2"d law, derive the pressure distribution inside water as a function of r and 0 in the cylindrical coordinate. (hint: use rectangular coordinate first, and then convert it to cylindrical coordinate). b) (20 pts) Use the surface integral method to compute the hydrostatic force acted on the 4th quadrant of the cylinder wall, as shown by the thickened line in the figure. c) (20 pts) Use control volume analysis and divergence theorem on the 4" quadrant water volume to compute the hydrostatic force acted on the same portion of the cylinder wall in b). Compare the result with that of b), they should be identical.